Weak compactness of unconditionally convergent operators on $C₀(T)$

Rok, strany: 2002, 57 - 66

Let $T$ be a locally compact Hausdorff space and let $C₀(T)$ be the Banach space of all complex valued continuous functions vanishing at infinity in $T$, provided with the supremum norm. Let $X$ be a locally convex Hausdorff space (briefly, an lcHs) which is quasicomplete. By using Rosenthal's lemma and the locally convex space analogue of the Bartle-Dunford-Schwartz representation theorem it is shown that every $X$@-valued unconditionally convergent operator on $C₀(T)$ is weakly compact. Then it is deduced that every continuous linear map $u: C₀(T)\to X$ is weakly compact if $c₀\not\subset X$.

ISO 690:

Panchapagesan, T. 2002. Weak compactness of unconditionally convergent operators on $C₀(T)$. In Mathematica Slovaca, vol. 52, no.1, pp. 57-66. 0139-9918.

APA:

Panchapagesan, T. (2002). Weak compactness of unconditionally convergent operators on $C₀(T)$. Mathematica Slovaca, 52(1), 57-66. 0139-9918.